" However, Euclid himself taught logic, and his pupil, Eubulides, who was famous for employing celebrated paradoxes, was the teacher of several later dialecticians.

" What value Eubulides and the other Megarian philosophers placed on these paradoxes is unclear, but the Megarians were very interested in the logic of whole propositions, in contrast to Aristotle's logic of predicates.

Euclid's pupils were said to have been Ichthyas, the second leader of the Megarian school ; Eubulides of Miletus ; Clinomachus ; and Thrasymachus of Corinth.

Eubulides (; fl.

These paradoxes were very well known in ancient times, some are alluded to by Eubulides ' contemporary Aristotle and even partially by Plato.

Eubulides as a 20th-century semanticist.

One version of the liar paradox is attributed to the Greek philosopher Eubulides of Miletus who lived in the 4th century BC.

Eubulides reportedly asked, " A man says that he is lying.

The paradox is so named because of its original characterization, attributed to Eubulides of Miletus.

Besides Ichthyas, Euclid's most important pupils were Eubulides of Miletus and Clinomachus of Thurii.

The Masked Man and The Horns, which are, however, also ascribed to Eubulides.

And so when Miss Langford came to teach at the one-room Chestnut school, where Jack was a pupil in the eighth grade, the Woman of Jack's mind assumed the teacher's face and figure.

He was crouched over his anvil in the courtyard getting his chisels into trim, when a splinter of steel flew into his eye and imbedded itself in his pupil.

An important formative influence was his elementary school teacher Mr Tachikawa, whose progressive educational practices ignited in his young pupil first a love of drawing and then an interest in education in general.

The most important was the study of the Peasants of Languedoc by Braudel's star pupil and successor Emmanuel Le Roy Ladurie.

Among the last of his labors was the defense of the orthodoxy of his former pupil, Thomas Aquinas, whose death in 1274 grieved Albertus ( the story that he travelled to Paris in person to defend the teachings of Aquinas can not be confirmed ).

He was the pupil and successor of Gorgias and taught at Athens at the same time as Isocrates, whose rival and opponent he was.

Pobedonostsev awakened in his pupil little love of abstract study or prolonged intellectual exertion, but instilled into the young man's mind the belief that zeal for Russian Orthodox thought was an essential factor of Russian patriotism to be cultivated by every right-minded emperor.

Among his collaborators was Giovanni Maria Butteri and his main pupil was Giovanni Bizzelli.

While Stradivari's first known violin states that he was a pupil of Amati, the validity of his statement is questioned.

He was a pupil of Proclus in Athens, and taught at Alexandria for most of his life, writing commentaries on Plato, Aristotle, and other philosophers.

The most famous pupil of Ammonius Saccas was Plotinus who studied under Ammonius for eleven years.

Anaximenes was a pupil of Zoilus and, like his teacher, wrote a work on Homer.

This master returned to Venice, where he soon afterwards died ; but by the high terms in which he spoke of his pupil to Falier, the latter was induced to bring the young artist to Venice, whither he accordingly went, and was placed under a nephew of Torretto.

Antonio began his musical studies in his native town of Legnago ; he was first taught at home by his older brother Francesco Salieri ( a former student of the violinist and composer Giuseppe Tartini ), and he received further lessons from the organist of the Legnago Cathedral, Giuseppe Simoni, a pupil of Padre Giovanni Battista Martini.

Salieri quickly impressed the Emperor, and Gassmann was instructed to bring his pupil as often as he wished.

Albrecht's brother, Erhard Altdorfer, was also a painter and printmaker in woodcut and engraving, and a pupil of Lucas Cranach the Elder.

His pupil, successor, and eventual biographer Rimbert considered the visions of which this was the first to be the main motivation of the saint's life.

" One notable pupil was Enoch Powell.

On 9 February 1953, Bedlington Grammar School pupil Charlton was spotted playing for East Northumberland schools by Manchester United chief scout Joe Armstrong.

It was one of two antiquities of Hamilton's collection drawn for him by Francesco Progenie, a pupil of Pietro Fabris, who also contributed a number of drawings of Mount Vesuvius sent by Hamilton to the Royal Society in London.

When he was a 16-year-old pupil at St Paul's School in London, the lines about Humphry Davy came into his head during a science class.

Lucien Pissarro was taught painting by his father, and described him as a “ splendid teacher, never imposing his personality on his pupil .” Gauguin, who also studied under him, referred to Pissarro “ as a force with which future artists would have to reckon ”.

The city hosted such leading lights as the mathematician Euclid and anatomist Herophilus ; constructed the great Library of Alexandria ; and translated the Hebrew Bible into Greek ( called the Septuagint for it was the work of 70 translators ).

300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the " Father of Geometry ".

Proclus introduces Euclid only briefly in his fifth-century Commentary on the Elements, as the author of Elements, that he was mentioned by Archimedes, and that when King Ptolemy asked if there was a shorter path to learning geometry than Euclid's Elements, " Euclid replied there is no royal road to geometry.

In the only other key reference to Euclid, Pappus briefly mentioned in the fourth century that Apollonius " spent a very long time with the pupils of Euclid at Alexandria, and it was thus that he acquired such a scientific habit of thought.

The only reference that historians rely on of Euclid having written the Elements was from Proclus, who briefly in his Commentary on the Elements ascribes Euclid as its author.

Although many of Euclid's results had been stated by earlier mathematicians, Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system.

Because this geometrical interpretation of multiplication was limited to three dimensions, there was no direct way of interpreting the product of four or more numbers, and Euclid avoided such products, although they are implied, e. g., in the proof of book IX, proposition 20.

In particular, it is thought that Euclid felt the parallel postulate was forced upon him, as indicated by his reluctance to make use of it, and his arrival upon it by the method of contradiction.

4th century BCE ) of Miletus was a philosopher of the Megarian school, and a pupil of Euclid of Megara.

Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use today.

We know from other references that Euclid ’ s was not the first elementary geometry textbook, but it was so much superior that the others fell into disuse and were lost.

Proclus ( 410-485 ), author of Commentary on the First Book of Euclid, was one of the last important players in Hellenistic geometry.

His edition of Euclid in 1543, the first translation of the Elements into any modern European language, was especially significant.

Over a millennium after Euclid, Ibn al-Haytham ( Alhazen ) circa 1000 AD conjectured that every even perfect number is of the form 2 < sup > p − 1 </ sup >( 2 < sup > p </ sup >− 1 ) where 2 < sup > p </ sup >− 1 is prime, but he was not able to prove this result.

" The phrase was used by many early Greek mathematicians, including Euclid and Archimedes.

" According to one of his biographers, al-Wahrani, Saladin was able to answer questions on Euclid, the Almagest, arithmetic, and law, but this was an academic ideal and it was study of the Qur ' an and the " sciences of religion " that linked him to his contemporaries.